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Integrals, Curl & force

  1. Nov 8, 2009 #1
    1. The problem statement, all variables and given/known data

    U(x,y) = 3x2 - 7y

    A) Calculate the force at the coordinate point (3,3)

    B) Determine if the following forces are conservative and find the change in potential energy correspoinding to each for an interval 0 to x

    i) Fx = ax + bs2 a and b are constants

    ii) Fx = AeBx (A and B are constants)

    c) a force F = 6i - 2j acts on a particle that undergoes a displacement of S = 3i + 5j

    i)find the work done by the force on the particle
    ii) find the angle between F and S
    2. Relevant equations



    3. The attempt at a solution

    Part A)

    by book says F(x,y) = -dU/dx i - dU/dy j those are partial derivatives

    so F = -6xi + 7j

    then F(3,3) = -18i + 7j and the magnitude is 19.31 N, the answer is given as 21.2 whats my mistake

    Part B)

    it says you need to take the curl and if it is 0, then it is conservative

    i) curl F = (-a - 2bx)j + (a + 2bx)k = 0

    ii) curl F = -ABeBx i + ABeBx k = 0

    Part C)

    i) W = F dot S = 18 - 10 = 8 N

    ii)thetaF = arctan -2/6 = -18.4 degress
    thetaS = artcan 5/3 = 59.0 degrees

    59.0-18.4 = 77.5 degrees
     
  2. jcsd
  3. Nov 8, 2009 #2

    rock.freak667

    User Avatar
    Homework Helper

    For part A

    when taking the partial derivative w.r.t.x you hold y as a constant

    so U= 3x2 - 7y
    ∂U/∂x= ∂/∂x(3x2 - 7y), so -7y is essentially treated like a constant.
     
  4. Nov 8, 2009 #3
    i did that dU/dx = 6x DU/dy = -7
     
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